This work aims to understand how eukaryotic cells are influenced in their direction and type of motion by the physical properties of their local environment, an important aspect of tissue development, wound healing, and cancer invasion. An experimentally tractable but powerful approach is to study cell motility on adhesive micropatterned substrates. Many experimental results are known, with no clear unified principles: why do fibroblasts prefer two- to one-dimensional substrates? What is the origin of periodic migration of zyxin-depleted fibrosarcomas on adhesive stripes? Why do some cell types crawl one way on an asymmetric pattern, while others crawl the opposite direction? These questions are difficult to answer because they involve the coupling of cell polarization, shape, and adhesion. We propose to develop quantitative physical models for fibroblasts and keratocytes crawling on adhesive micropatterns and pushing through complex environments. These models will couple chemical polarization through reaction-diffusion mechanisms, cell shape and mechanics controlled by actin polymerization and myosin contractility, and the effects of the adhesive geometry. We will refine these models based on experimental measurements of actin retrograde flow and cell traction forces in cells on micropatterns, before and after chemical interventions such as myosin inhibition. This model will help provide an increased understanding of the controlling factors of motility and polarization on micropatterns, as well as the more general question of how cells respond to their local microenvironment, which we will study by introducing obstacles to cell motion. Understanding these factors may eventually lead to increased control of these behaviors and better tools for preventing cancer metastasis.